The subject application relates to document scanner calibration systems and methods. While the systems and methods described herein relate to document scanners and the like, it will be appreciated that the described techniques may find application in other scanning systems, other xerographic applications, and/or other calibration methods.
Document scanners generally produce a fixed number of bits (e.g., 8) per separation, forcing their values to be within a specific range. One design parameter that affects scanner calibration is the level to which the “white” value of a calibration strip translates when the calibration is applied. Using classical approaches, values brighter than the white calibration value are clipped. A very small amount of clipping is desirable in most applications, since for all but the very few pixels clipped, the image has a higher dynamic range. However, when a scanner is used as a surrogate for a spectrophotometer, for example, clipped pixels contribute to erroneous patch averages. Classical approaches address such errors in several ways. For instance, one approach is to ignore the problem and trust a data fitting technique to reduce its effect. Another approach is to discard patches containing any clipped pixels. Yet another approach involves using a scanner with less gain, and therefore less (or no) chance of clipping any pixels, which has the undesirable effect of reducing dynamic range, and hence the number of actual brightness levels available.
In at least one scanner, 10-bit values are generated by a digital to analog converter and these values are converted to 8 bit values when a calibration process is applied. Accuracy at the dark end of the brightness spectrum is limited both by quantization and noise. It is difficult to reduce noise without increasing the cost of the scanner, other than by increasing the number of pixels averaged. However, in the process of converting from 10 bit digital-to-analog conversion (DAC) values to 8 bit scan values, the measured values are translated and scaled based on values obtained in a calibration and fixed parameters. Assuming a white calibration strip is perfectly uniform, the values are scaled so that the value read from the white calibration strip is W, which is an adjustable (by the manufacturer) parameter. Setting the value of W too low increases quantization error, particularly at the dark end (e.g., choosing a value of 100 means that there is a single step between 1% and 2%, whereas setting W equal to 400 increases this to four steps); setting W too high increases clipping (e.g., if W is 255, then any pixels that receive more light than the calibration strip will be clipped, as will any which, due to noise, would otherwise register values greater than 255).
According to an example, a scanner, when measuring a patch of white paper in a random surround, detects a mean value around 244 with a standard deviation around 5.7, with the default setting of W. While the reported mean white value is substantially below 255, it is to be expected that any patch of, for instance, 50×50 pixels will have a substantial number of pixels that register at values greater than 255 (e.g., approximately 2.5%, or 60 pixels). Due to integrating cavity effect, lighter surrounds will increase the number of saturated pixels, while darker surrounds will decrease the number. Statistically, it would be expected that the vast majority of these saturated pixels would be no greater than 244+3×5.7=244+17.1=261.1 (that is, all but 0.13% of the total, or 3 pixels). Even with all pixels at an improbably large value such as 261, the error in the mean due to these 60 or so pixels being underestimated by 6/255, is only 0.15 (0.06 is more typical), while the estimated error in the mean (i.e., the standard error of the mean) is 0.114. A small increase in W could make this significant: if all the true values were scaled and then clipped so that the mean of the unclipped values would be 250, the standard deviation would scale to 5.87, which means that nearly 20% of the pixels will be clipped, with an error of approximately 0.64, which is substantially greater than the standard error of the mean.
The error resulting from clipping generally increases as the number of pixels clipped increases, rising slowly until the number approaches 50% of the pixels. For a theoretical example of 2500 normally-distributed pixels, with a mean value of 244, the quantization error rises exponentially.
In reality, the distribution is not normal (e.g., for white paper it might be close, but for light patches containing a small amount of toner it will be bi-modal). However the principle still holds: as the number of pixels clipped increases, the error in the mean increases exponentially, and even for relatively small numbers of clipped pixels, it increases.
Accordingly, there is an unmet need for systems and/or methods that facilitate compensating for clipping in input scanners and the like, while overcoming the aforementioned deficiencies.